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Which describes the system of equations below? $\newline$ $y = \frac{8}{7}x + \frac{10}{9}$ $\newline$ $y = \frac{8}{7}x + \frac{10}{9}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (C)consistent and independent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = \frac{8}{7}x + \frac{10}{9}

\newline

y = \frac{8}{7}x + \frac{10}{9}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Compare Slopes: We have the system of equations: $\newline$ y = $(\frac{8}{7})x + (\frac{10}{9})$ $\newline$ y = $(\frac{8}{7})x + (\frac{10}{9})$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = (\frac{8}{7})x + (\frac{10}{9})$ , the slope is $\frac{8}{7}$ . $\newline$ In $y = (\frac{8}{7})x + (\frac{10}{9})$ , the slope is also $\frac{8}{7}$ . $\newline$ Since the slopes are the same, we can say that the lines are parallel or coincident.
Compare Y-Intercepts: Next, we need to compare the y-intercepts of both equations. $\newline$ In $y = \frac{8}{7}x + \frac{10}{9}$ , the y-intercept is $\frac{10}{9}$ . $\newline$ In $y = \frac{8}{7}x + \frac{10}{9}$ , the y-intercept is also $\frac{10}{9}$ . $\newline$ Since the y-intercepts are the same, we can say that the lines are coincident.
Conclusion: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are the same line. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions. $\newline$ The system of equations is consistent because there are solutions, and it is dependent because the equations describe the same line.

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